The classical porous media equation is obtained by setting \(\tau = 0\) 
and by replacing (REF ) by the algebraic law
\(p=p_c(s)\) . This classical equation is interesting when the
permeability coefficient is degenerate \(k(0) = 0\) . For existence and
uniqueness results in this classical case we refer to [1]}, [2]}. The hysteresis model (REF ) was
introduced in [3]}, [4]}, [5]}. It combines dynamic effects
(\(\tau >0\) ) with a play-type hysteresis relation; the latter allows for
an interval of pressure values \(p\)  for a fixed saturation \(s\) . For a
review of the modelling, we refer to [6]}.
